The certification flights, which are expected to take approximately three days, represent a key step in the eventual ungrounding of the plane that was involved in two fatal crashes that killed a total of 346 people.
Ethiopian Airlines Flight 302 crashed near Addis Ababa airport just six minutes after takeoff, killing all on board, in March 2019. It was the second crash involving a Boeing 737 Max within five months. In October 2018, Lion Air Flight 610 was airborne for only 13 minutes before it plunged into the Java Sea off the coast of Indonesia.
The similarities between the two crashes raised questions about the safety of Boeing's once fastest-selling jet. Countries around the world began grounding the plane, and, on March 13, 2019, the FAA grounded the Max in the United States.
Investigators found that both crashes were tied to a software called the Maneuvering Characteristics Augmentation System (MCAS). MCAS was designed to help stabilize the 737 Max after heavier, re-positioned engines placed on the aircraft caused the plane's nose to point too far upwards in certain circumstances.
In both crashes, incorrect data from a faulty sensor caused MCAS to misfire, forcing the plane to nose down repeatedly even as pilots struggled to regain control and gain altitude. MCAS was not mentioned in the pilot manual.
In December, House Democrats released a FAA risk report which showed the potential of more than 15 fatal crashes over the life of the Max fleet -- about 45 years -- if no change was made to MCAS.
Boeing decided to not just rewrite the software for the MCAS flight control system, but the entire flight computer software. The manufacturer discovered additional software and wiring problems unrelated to the crashes in the process.
The flight tests this week "will include a wide array of flight maneuvers and emergency procedures to enable the agency to assess whether the changes meet FAA certification standards," according to a letter the FAA sent to oversight committee staffers Sunday.
However, even if they are successful, it is unlikely the MAX will be ungrounded before September, sources familiar with the matter explained.
"While the certification flights are an important milestone, a number of key tasks remain," the FAA said in a statement. "The FAA is following a deliberate process and will take the time it needs to thoroughly review Boeing's work. We will lift the grounding order only after we are satisfied that the aircraft meets certification standards."
The two fatal 737 MAX crashes sparked multiple investigations from U.S. agencies, including the Department of Justice and the Securities and Exchange Commission.
Gary Kelly, the CEO of the largest U.S. operator of the Max, Southwest, has said he expects the Max will return to service by the end of the fourth quarter.
Arguably, the toughest task will be winning back the public's trust.
"The 737 MAX, or whatever it's called in the future, will be a great airplane, but it will take time. People are not going to be happy getting on the MAX-branded aircraft, " ABC News Contributor and retired Marine Col. Steve Ganyard said.